Question

Find the equation of the line passing through the point (1,3) and perpendicular to the line 2x + 5y = 4.  Write your answer in general form.  Do not use any space between the letter (lower case), symbol and number, say x+y-1=0

Answer 1

5y=-2x+4 so the slope is -⅖. The gradient of the perpendicular is the negative reciprocal: 5/2 and the general equation of the perpendicular is y=5x/2+a where a is a constant. For (1,3) to be on this line:

3=5/2+a, making a=3-5/2=½. So y=5x/2+1/2 or 2y=5x+1, 5x-2y+1=0 in general form.